Variance Components Of Random Effects Research Articles

Association Test for X-Linked QTL in Family-Based Designs

Family-based association methods for detecting quantitative trait loci (QTL) have been developed primarily for autosomes, and comparable methods for X-linked QTL have received less attention. We have developed a family-based association test for quantitative traits, named XQTL, which uses X-linked markers in a nuclear family design. XQTL adopts the framework of the orthogonal model implemented in the QTDT program, modifying the sex-specific score for X-linked genotypes. XQTL also takes into account the dosage effect due to female X chromosome inactivation. Restricted maximum likelihood (REML) and Fisher's scoring method are used to estimate variance components of random effects. Fixed effects, derived from the phenotypic differences among and within families, are estimated by the least-squares method. Our proposed XQTL can perform allelic and two-locus haplotypic association tests and can provide estimates of additive genetic effects and variance components. Simulation studies show correct type I error rates under the null hypothesis and robust statistical power under alternative scenarios. The loss of power observed when parental genotypes are missing can be compensated by an increase of offspring number. By treating age at onset of Parkinson disease as a quantitative trait, we illustrate our method, using MAO polymorphisms in 780 families.

Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.

Generalized p-Values and Generalized Confidence Intervals for Variance Components in General Random Effect Model with Balanced Data

Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type I error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type I error probability.

An Illustration of the Consequences of Meta-Analysis Model Choice

Fixed- and random-effects models represent two different approaches to analyzing and understanding data with meta-analysis. The current article describes the results of a two-part study to illustrate the effect of choice of meta-analytic model on study conclusions. Part 1 illustrates the effect of model choice by analyzing data simulated to conform to either fixed- or random-effects scenarios with both fixed- and random-effects methods of data analysis. Part 2 uses two published meta-analyses to show that methodological choices, in this case mainly the choice of fixed- or random-effects models, affect estimates both of mean effect size and of the random-effects variance component (REVC). Overall, results suggest that random-effects procedures represent the best initial choice when conducting a meta-analysis.

How to Meta-Analyze Coefficient-of-Stability Estimates

Reliability generalization studies have provided estimates of the mean reliability coefficients and examined factors that explain the variability in the reliability estimates across studies for many different tests and measures. Different authors have used different data analyses to do such meta-analyses, and little research has addressed whether some methods are more accurate than others. Three methods of meta-analysis for reliability data were compared using Monte Carlo techniques. The meta-analytic methods were those described by Hedges and Vevea, Hunter and Schmidt, and Vacha-Haase. The results suggested that a combination of methods worked best and that Hunter and Schmidt's method should be used to estimate the mean and random-effect variance component, but weighted regression should be used to model continuous moderators.

A Note on Permutation Tests for Variance Components in Multilevel Generalized Linear Mixed Models

In many applications of generalized linear mixed models to multilevel data, it is of interest to test whether a random effects variance component is zero. It is well known that the usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In this note we propose a permutation test, based on randomly permuting the indices associated with a given level of the model, that has the correct Type I error rate under the null. Results from a simulation study suggest that it is more powerful than tests based on mixtures of chi-square distributions. The proposed test is illustrated using data on the familial aggregation of sleep disturbance.

The limiting distribution of the F-statistic from nonnormal universes

We consider a linear regression model with an unbalanced 1-fold nested error structure, where group effect and error are from nonnormal universes. The limiting distribution of the F-statistic in this model is derived, as the sample size is large and group sizes take values from a finite set of distinct integers. The result is used to approximate the F-distribution quantile and to test the significance of the random effect variance component. Results are also applicable to the F-statistic in the one-way random-effects model. The effects of departure from normality on the F-statistic distribution are given.

A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models

This article is about testing the equality of several normal means when the variances are unknown and arbitrary, i.e., the set up of the one-way ANOVA. Even though several tests are available in the literature, none of them perform well in terms of Type I error probability under various sample size and parameter combinations. In fact, Type I errors can be highly inflated for some of the commonly used tests; a serious issue that appears to have been overlooked. We propose a parametric bootstrap (PB) approach and compare it with three existing location-scale invariant tests—the Welch test, the James test and the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test is the best among the four tests with respect to Type I error rates. The PB test performs very satisfactorily even for small samples while the Welch test and the GF test exhibit poor Type I error properties when the sample sizes are small and/or the number of means to be compared is moderate to large. The James test performs better than the Welch test and the GF test. It is also noted that the same tests can be used to test the significance of the random effect variance component in a one-way random model under unequal error variances. Such models are widely used to analyze data from inter-laboratory studies. The methods are illustrated using some examples.

Intramyocellular Lipid Quantification: Repeatability with1H MR Spectroscopy

To prospectively determine the repeatability and variability of tibialis anterior intramyocellular lipid (IMCL) quantifications performed by using 1.5-T hydrogen 1 (1H) magnetic resonance (MR) spectroscopy in healthy subjects. Institutional review board approval and written informed consent were obtained for this Health Insurance Portability and Accountability Act-compliant study. The authors examined the anterior tibial muscles of 27 healthy subjects aged 19-48 years (12 men, 15 women; mean age, 25 years) by using single-voxel short-echo-time point-resolved 1H MR spectroscopy. During a first visit, the subjects underwent 1H MR spectroscopy before and after being repositioned in the magnet bore, with voxels carefully placed on the basis of osseous landmarks. Measurements were repeated after a mean interval of 12 days. All spectra were fitted by using Java-based MR user interface (jMRUI) and LCModel software, and lipid peaks were scaled to the unsuppressed water peak (at 4.7 ppm) and the total creatine peak (at approximately 3.0 ppm). A one-way random-effects variance components model was used to determine intraday and intervisit coefficients of variation (CVs). A power analysis was performed to determine the detectable percentage change in lipid measurements for two subject sample sizes. Measurements of the IMCL methylene protons peak at a resonance of 1.3 ppm scaled to the unsuppressed water peak (IMCL(W)) that were obtained by using jMRUI software yielded the lowest CVs overall (intraday and intervisit CVs, 13.4% and 14.4%, respectively). The random-effects variance components model revealed that nonbiologic factors (equipment and repositioning) accounted for 50% of the total variability in IMCL quantifications. Power analysis for a sample size of 20 subjects revealed that changes in IMCL(W) of greater than 15% could be confidently detected between 1H MR spectroscopic measurements obtained on different days. 1H MR spectroscopy is feasible for repeatable quantification of IMCL concentrations in longitudinal studies of muscle metabolism.

Generalized estimating equations for longitudinal mixed Rasch model

In this paper, the problem of estimating the fixed effects parameters and the variance of the random effects (variance components) in longitudinal mixed Rasch model is considered. It is well known that estimating these parameters by the method of maximum likelihood faces computational difficulties. As an alternative, we propose the generalized estimating equations approach. Approximations of the joint moments of the variables are proposed. The estimators obtained are consistent and asymptotically normal. We illustrate the usefulness of the method with simulations and with an analysis of real data from quality of life.

Multilevel linear modelling for FMRI group analysis using Bayesian inference

Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and top-level regression parameters. Due to the typically small numbers of sessions or subjects in neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an information-theoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.

The Effect of Design Imbalance on the Power of the F‐test of a Variance Component in the One‐Way Random Model

AbstractThe ANOVA‐based F‐test used for testing the significance of the random effect variance component is a valid test for an unbalanced one‐way random model. However, it does not have an uniform optimum property. For example, this test is not uniformly most powerful invariant (UMPI). In fact, there is no UMPI test in the unbalanced case (see Khuri, Mathew, and Sinha, 1998).The power of the F‐test depends not only on the design used, but also on the true values of the variance components. As Khuri (1996) noted, we can gain a better insight into the effect of data imbalance on the power of the F‐test using a method for modelling the power in terms of the design parameters and the variance components. In this study, generalized linear modelling (GLM) techniques are used for this purpose. It is shown that GLM, in combination with a method of generating designs with a specified degree of imbalance, is an effective way of studying the behavior of the power of the F‐test in a one‐way random model.

Estimation of farm specific parameters in a longitudinal model for litter size with variance components and random dropout

The estimation of farm specific parameters is often ignored in studies of decision support systems such as, e.g., sow replacement problems. This study concerns the specification and estimation of farm specific parameters in a model for litter size required by a replacement problem considering culling based on productive performance. This implies a joint distribution of the litter size at the parities under consideration. A non-linear parametric mean curve is used to model the expected litter size at different parities for sows within the same herd. The covariance matrix is modeled using variance components of random effects, serial correlation and measurement error. Data from a total of 43 herds are used to devise a likelihood based inference, using maximum likelihood to obtain initial estimates for maximum posterior estimation of farm specific parameters. The maximum posterior approach is required to obtain reasonable estimates in the cases where on-farm registrations are inadequate.

Mixed effects logistic regression models for multiple longitudinal binary functional limitation responses with informative drop-out and confounding by baseline outcomes.

In the context of analyzing multiple functional limitation responses collected longitudinally from the Longitudinal Study of Aging (LSOA), we investigate the heterogeneity of these outcomes with respect to their associations with previous functional status and other risk factors in the presence of informative drop-out and confounding by baseline outcomes. We accommodate the longitudinal nature of the multiple outcomes with a unique extension of the nested random effects logistic model with an autoregressive structure to include drop-out and baseline outcome components with shared random effects. Estimation of fixed effects and variance components is by maximum likelihood with numerical integration. This shared parameter selection model assumes that drop-out is conditionally independent of the multiple functional limitation outcomes given the underlying random effect representing an individual's trajectory of functional status across time. Whereas it is not possible to fully assess the adequacy of this assumption, we assess the robustness of this approach by varying the assumptions underlying the proposed model such as the random effects structure, the drop-out component, and omission of baseline functional outcomes as dependent variables in the model. Heterogeneity among the associations between each functional limitation outcome and a set of risk factors for functional limitation, such as previous functional limitation and physical activity, exists for the LSOA data of interest. Less heterogeneity is observed among the estimates of time-level random effects variance components that are allowed to vary across functional outcomes and time. We also note that. under an autoregressive structure, bias results from omitting the baseline outcome component linked to the follow-up outcome component by subject-level random effects.

Additive genetic and environmental variance components for milk traits in goat with test day model

Genetic and environmental dispersion parameters for daily milk yield (DMY), fat (FC), protein (PC) and lactose contents (LC) were estimated on 1805 does of Alpine and Saanen breed. During the period 1991-1996, 24044 monthly test days were obtained from 57 herds in Slovenia. (Co)variance components for random effects and residual were estimated by REML using Powell’s algorithm. The models contained season (year-month interaction) and breed as fixed effects, litter size, day of lactation and parity as independent variables, and common flock, permanent environment and additive genetic effect (animal) as random effects. Heritability for DMY was 0.19 - 0.20, for FC was 0.16 - 0.18, for PC was 0.21 - 0.24, and for LC was 0.21 - 0.23. The greatest part of phenotypic variance of FC, PC and LC remained in residual. FC and PC had a negative genetic correlation with DMY (-0.32 and -0.41). Correlation between FC and PC was positive (+0.57), as between PC and LC (+0.27).

Assessing Interrater Agreement from Dependent Data

Estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods. We investigate the use of a latent model proposed by Qu, Piedmonte, and Medendorp (1995, Biomerics 51, 268-275) to estimate the correlation between raters for each method, and test for their equality. For each of the assessment methods, these correlations can be interpreted as the variance components of random effects representing subject and rater. This method is applied to an HIV study, in which the amount of ectopy on a woman's cervix is measured by both direct visual assessment and a computer planimetry method.

A multivariate approach for estimating the random effects variance component in one-way random effects model

It is well known that the ANOVA estimator of the random effects variance component in one-way random effects model can assume negative values. It is also well known that nonnegative quadratic unbiased estimators do not exist for estimating the random effects variance component (LaMotte, 1973). LaMotte (1985) indicated the possibility that nonnegative invariant quadratic estimator of the random effects variance component uniformly better than the ANOVA estimator may exist for the balanced one-way random effects model. Mathew et al. (1992a) have shown that such estimator exists only when the number of treatments is 9 or less. As noted in Herbach (1959) (see also Thompson, 1962), a simple truncation of the ANOVA estimator at zero yields uniform improvement over the ANOVA estimator. The estimators suggested by Herbach and Thompson are, in fact, restricted maximum likelihood estimators, and they are nonquadratic by nature. In this paper, we discuss a multivariate technique which always yields positive estimate of the random effects variance component in one-way random effects model. The multivariate approach exploits the estimates of the eigenvalues of the covariance matrix of the model in estimating the variance components including the error variance. The resulting estimates are nonquadratic. The success of this multivariate approach depends on the precise estimation of the eigenvalues. Since there does not exist any unbiased estimation procedure in the small sample case for the estimation of the eigenvalues, we use a delete-d jackknife procedure to estimate them. This delete-d jackknife based multivariate approach yields better estimates (in terms of mean squared error) for the random effects variance component than the restricted maximum likelihood estimation as well as Chow and Shao's (1988) nonquadratic estimation approaches, which is shown through a simulation study for the cases with number of treatments up to 20.

Evaluation of line and breed of cytoplasm effects on performance of purebred Brangus cattle.

Substantial differences between reciprocally crossed Bos taurus x Bos indicus calves for birth, weaning, and yearling weights have been reported. To determine whether cytoplasmic inheritance is responsible for a portion of these differences, field records for birth and weaning weight (n = 7,353) and postweaning average daily gain (n = 2,746) from registered Brangus calves were analyzed. An animal model that included maternal effects was fit for each trait. Breed of cytoplasmic origin was fit as a fixed effect and coded as Angus, Brahman, or unknown. Cytoplasmic line within each breed of origin was treated as a random effect. Variance components for random effects were estimated using derivative-free REML procedures. Line of cytoplasm accounted for less than .002% of the phenotypic variance in all three traits. Estimates for cytoplasmic breed of origin effects were small in magnitude, and contrasts tested (Angus vs Brahman and Angus vs Unknown) were not significant (P > .10). Estimates of heritability of direct (maternal) effects were .36 (.20), .41 (.27), and .21 (.08) for birth weight, weaning weight, and postweaning average daily gain, respectively. Estimates of genetic correlations between direct and maternal effects ranged from -.27 for postweaning average daily gain to -.58 for birth weight. No evidence for breed or line within breed of cytoplasmic origin effects was detected in these data.

Some Tests for Variance Components Using GeneralizedpValues

The concept of a generalized p value, introduced by Tsui and Weerahandi, is applied for testing hypotheses in two situations, testing the significance of a variance component in a general balanced mixed model when an exact F test does not exist and comparing randomeffects variance components in two independent balanced mixed models. Extensions to the unbalanced cases are also indicated. The proposed test is compared with the test based on the Satterthwaite approximation through their simulated Type I error probabilities. The simulations indicate that the test based on the generalized p value hasType I error probabilities less than the chosen significance level most of the time, whereas the Type I error probabilities of the Satterthwaite approximate test can be much larger than the significance level. The results are illustrated using two examples.

Improved Nonnegative Estimation of Variance Components in Some Mixed Models with Unbalanced Data

Mixed models involving two variance components are considered when the data are unbalanced, one variance component corresponding to a random effect and a second variance component corresponding to experimental error. For estimating the random-effect variance component, several nonnegative estimators are derived. The estimators have explicit expressions and are easily computable. The performances of the various estimators are studied by simulating their mean squared errors and biases using some one-way models with unbalanced data, and specific recommendations are made on the choice of the nonnegative estimator to be used in practical applications. Some generalizations are obtained for estimating a randomeffect variance component in a more general model with unbalanced data. The analysis of variance (ANOVA) estimator and the proposed estimators are computed using real data for two examples. The ANOVA estimator has a value that is substantially different from the other estimators in the two examples. The simulation results and the examples suggest that the ANOVA approach should not be used for obtaining point estimates of variance components; instead, the more efficient procedures developed in this article should be preferred.